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Exercise

$\int\left(\frac{5u}{\sqrt{u-8}}\right)dx$

Step-by-step Solution

1

Take out the constant $5$ from the integral

$5\int\frac{u}{\sqrt{u-8}}dx$
2

The integral of a constant is equal to the constant times the integral's variable

$5\left(\frac{u}{\sqrt{u-8}}\right)x$
3

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$5\left(\frac{u}{\sqrt{u-8}}\right)x+C_0$

Final answer to the exercise

$5\left(\frac{u}{\sqrt{u-8}}\right)x+C_0$

Try other ways to solve this exercise

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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